Can you not try to lighten the trigger yourself, usually there are a few how to videos etc, that show you what to do.
You had better know what you're doing with a BLR. It has a rather difficult to adjust/hone linkage. The Savage 99 is touchy in that it is easy to take to much off the sear, the BLR because of its linkage is worse. Much of the drag comes from the linkage itself rather than the sear.
As far as shouldering to well, to me that just means the shooter found a rifle that fit him properly.
Some people just like lever actions. IMHO the BLR is one of the better lever action rifles because of its strength. I don't particularly like Browning rifles because they are a pain to get parts for and can be extremely fussy with ammo they like. Plus a myriad of other things.
I have seen the odd Browning shoot extremely well but most are just average at best. The BLR on the other hand is capable of very good accuracy right out of the box.
OP, I suspect your problem is more flinch than a heavy/creepy trigger. Shooting offhand is seldom a long drawn out process of deliberation. It is meant to be quick and close enough. Some people on the other hand are phenomenal off hand shots.
About 20 years ago I tried to put on off hand turkey shoots. I was extremely lucky if 3 or 4 people showed up and usually they shot muzzle loaders or single shot rifles. We had a lot of fun but I can tell you the competition was brutal. Very few shooters practice their offhand skills appropriately. This is to bad because a lot of animals get wounded to die a lingering death rather than be killed cleanly as is their right and our obligation to them.
I would suggest you pick up a BLR22 and scope it identically to your BLR center fire rifle. The trigger pulls are similar and I think some extended practice would do you a lot more good than a trigger job.